Indra's Pearls: The Vision of Felix Klein

by David Mumford , Caroline Series , David Wright

• ISBN13: 9780521352536
• ISBN10: 0521352533
• Format: Hardcover
• Copyright: 2002-05-06
• Publisher: Cambridge University Press

Summary

Felix Klein, one of the great nineteenth-century geometers, rediscovered in mathematics an idea from Eastern philosophy: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple co-existing symmetries. For a century these ideas barely existed outside the imagination of mathematicians. However in the 1980s the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.

Table of Contents

1. The language of symmetry

2. A delightful fiction

3. Double spirals and Mö

bius maps

4. The Schottky dance

5. Fractal dust and infinite words

6. Indra's necklace

7. The glowing gasket

8. Playing with parameters

9. Accidents will happen

10. Between the cracks

11. Crossing boundaries

12. Epilogue

Index

Road map.